A year ago, Jasper Inc. sold 20-year bonds at par with a coupon rate of 4.5 percent and semiannual payments. The face value of each bond is $1,000 and the yield to maturity is now 5.6 percent. What is the current value of each bond?

= $877.32

Explanation:

The value of the bond is the present value (PV) of the future cash receipts expected from the bond. The value is equal to present values of interest payment plus the redemption value (RV).

Value of Bond = PV of interest + PV of RV

The value of bond for Jasper Inc can be worked out as follows:

Step 1

PV of interest payments

Semi annul interest payment

= 4.5% * 1000 * 1/2

= 22.5

Semi-annual yield = 5.6/2 = 2.8% per six months

Total period to maturity (in months)

= (2 * 19) = 38 periods (Note it was sold a year ago)

PV of interest =

22.5 * (1 - (1+0.028) ^ (-38) / 0.028)

= 22.5 * 23.20871226

= 522.196

Step 2

PV of Redemption Value

= 1,000 * (1.056) ^ (-19)

= 355.128

Price of bond

= 522.19 + 355.12

= $877.32